• I'll use "measurement error" in a broad way, also including misclassifications as a special case

• Measurement error: sensitivity and/or specificity \(< 1\)

• Review of 57 epidemiology papers found 'only' 61% mentioning measurement error in exposure

Measurement error mentioned (exposure/confounder) as possible important factor? Yes:

• 56% in top-ranked epidemiology journals (N = 337)
  Am J Epidemiol, Epidemiology, Eur J Epidemiol, Int J Epidemiol, J Clin Epidemiol, J Epidemiol Community Health
• 25% in top-ranked general medicine journals (N = 228)
  NEJM, JAMA, Lancet, BMJ, Ann Intern Med

• 18 articles used methods to correct for or investigate impact of measurement error (3% of total, 7% of those mentioning measurement error)

• Rife with unsubstantiated claims about anticipated impact of measurement error

• Myths

1. Measurement error is often random
2. Measurement error can be compensated by large data
3. Measurement error attenuates exposure effects
4. Measurement error affects only certain types of research
5. Measurement error can be solved by simple logical rules or averaging
6. Measurement error can be prevented but not mitigated

• Simple situation: there is a true measurement for each individual \(i\), (\(T_i\)), and there is a corresponding error contaminated measurement (\(X_i\))

• Classical ("random") measurement error model
  \(X_i = T_i + e_i, \quad e \sim N(0,\sigma^2)\)
• Systematic measurement error model
  \(X_i = \lambda T_i + e, \quad e\sim N(\alpha,\tau^2)\)

• Differential measurement error: the magnitude of error (error variance) depends on other key variables

• Heteroscedastic measurement error: the magnitude of error depends on the true values of what is measured

• Berkson measurement error: \(T_i = X_i + e_i\)

• Easy to get lost in the terminology

Measurement error is completely random if the errors in measurement have a constant variance around their true value, are independent of this true value and other observed or unobserved patient characteristics, and the measurements with error are on the same scale as the true values (no systematic error)

SBP measurement error may depend:

• White coat effect (1)
• Gender effect (2)
• Number of BP measurements (2)
• BP measurement instrument (3)
• Adherence to measurement protocol (4)
• etcetera.

Random measurement error?

Larger \(N\):

• can compensate for reduced precision of exposure effect estimate due to measurement error

Large \(N\) has no effect on:

• Measurement error bias in exposure effect estimate
• Measurement error masking of functional relations

Larger data sets: more precisely wrong?

• Attenuation bias is defined as an expectation

To claim attenuation bias:

• The error is in the exposure
• Exposure is not a categorical variable with \(>2\) categories
• The error is classical error
• The linear model applies (e.g. it's not logistic regression)*
• There are no other variables measured with error in the model

• Cox proportional hazards models
• Added simulated random measurement error to 1 exposure and 1 confounder variable

• Traditional epidemiologic research: observational, etiologic/therapeutic oriented

• Randomized (controlled) trials

• Prognostic modeling studies

• If measurement error is random: "only" loss of power
• If measurement error is not random: loss of power, inflated type-I error and bias in effect estimator

• Predictor variables with measurement error are generally worse predictors
• Development-validation difference in measurement error can impact predictive performance

• Prediction model calibration strongly affected by development-validation difference in measurement error

The idea is that multiple measurements with error of the same phenomenon are likely to increase the overall accuracy of measurement when we combine them. Often by averaging/sums or simple logical rules.

• Multiple survey items for same construct

• Multiple blood pressure measurements for blood pressure

• Multiple diagnostic tests for the same disease

• A priori defined logistic rule based on multiple test results to improve disease verification

• Composite reference standards never completely remove all of the measurement error

• Disease verification by composite reference standard can be worse than an individual test in the rule

Measurement of the variables with error (X) with/without truth (T) in an internal/external subset

• Regression calibration: "X" is replaced by a prediction of "T"

• SIMEX: Additional error is simulated and added to "X", extrapolation is used to estimate the effect without error in "X"

• MIME: "T" is multiple imputed for individuals for whom "T" wasn't observed

• Latent variable models: multiple measures of "X" to approximate "T"

• Measurement error in the outcome of a prediction model (no gold standard)

• User friendly software (https://github.com/LindaNab/mecor)

• Approaches that address complex measurement error structures in multiple variables

• Unified approaches to simultaneously correct for measurement error, confounding and missing values

Myth 1: Measurement error is often random

measurement error is seldom truly random

Myth 2: Measurement error can be compensated by large data

large \(N\) alleviates only one aspect of measurement error issues

Myth 3: Measurement error attenuates exposure effects

generally difficult to predict impact of measurement error without explicit theorizing and modeling

Myth 4: Measurement error affects only certain types of research

it is very unlikely that, if present, measurement error doesn't affect research findings

Myth 5: Measurement error can be solved by simple logical rules or averaging

too simple solution for a complex problem

Myth 6 Measurement error can be prevented but not mitigated

better to prevent than to cure measurement error. There are plenty of correction methods available if measurement error can't be prevented. We probably should start using them more

The myths about measurement error contribute to a tolerant attitude towards measurement error, they seem founded on misconceptions that measurement errors have limited impact on results of epidemiologic research. Notably, the misconception that bias is towards the null effect may unrightfully reassure that one is protected against overestimating effects.